-8x^2-80x=-24

Solution for -8x^2-80x=-24 equation:

-8x^2-80x=-24

We move all terms to the left:

-8x^2-80x-(-24)=0

We add all the numbers together, and all the variables

-8x^2-80x+24=0

a = -8; b = -80; c = +24;
Δ = b2-4ac
Δ = -802-4·(-8)·24
Δ = 7168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-32\sqrt{7}}{2*-8}=\frac{80-32\sqrt{7}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+32\sqrt{7}}{2*-8}=\frac{80+32\sqrt{7}}{-16}
$